Julia Stadlmann

Sieve theory and gaps between primes

The behaviour of gaps between primes is subject to many conjectures, proofs of which often seem far out of reach. In the past couple of decades, sieve theory has helped make the disparity between what we believe to be true and what we know to be true just a little smaller. In this talk, I will give an introduction to the basic ideas and techniques of sieve theory and outline how a modern method, known as Harman's sieve, can be used to improve a bound on the average size of the squares of gaps between primes.